Extensions of the Carlitz-McConnel and Blokhuis-Sziklai theorems for unions of cyclotomic classes

Maosheng Xiong, Chi Hoi Yip

Let $p$ be a prime, let $q=p^n$, and let $D\subseteq {\mathbb{F}}_q^{\ast }$. A celebrated result of Carlitz and McConnel states that if $D$ is a proper subgroup of ${\mathbb{F}}_q^{\ast }$,…